Conformal geometry of discrete groups and manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; New York
<<de>> Gruyter
2000
|
| Series: | De Gruyter expositions in mathematics
32 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 461 - 511 |
| Physical Description: | XIII, 523 S. graph. Darst. : 25 cm |
| ISBN: | 3110144042 |
Staff View
MARC
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| 100 | 1 | |a Apanasov, Boris Nikolaevič |d 1920- |e Verfasser |0 (DE-588)105576724X |4 aut | |
| 245 | 1 | 0 | |a Conformal geometry of discrete groups and manifolds |c by Boris N. Apanasov |
| 264 | 1 | |a Berlin ; New York |b <<de>> Gruyter |c 2000 | |
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| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a De Gruyter expositions in mathematics |v 32 | |
| 500 | |a Literaturverz. S. 461 - 511 | ||
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| 650 | 7 | |a Géométrie conforme |2 ram | |
| 650 | 7 | |a Variétés (Mathématiques) |2 ram | |
| 650 | 4 | |a Conformal geometry | |
| 650 | 4 | |a Discrete groups | |
| 650 | 4 | |a Manifolds (Mathematics) | |
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Record in the Search Index
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Table of Contents
Preface vii
1. Geometric Structures 1
1.1. (X, G) structures on manifolds 1
1.2. Conformal geometry on the sphere 4
1.3. The hyperbolic space H" 11
1.4. Lie subgroups of the Mobius group 19
1.5. Structure developments and holonomy homomorphisms 22
1.6. The eight 3 dimensional geometries 25
1.7. Four dimensional geometries 31
1.8. Geometry of orbifolds 33
Notes 39
2. Discontinuous Groups of Homeomorphisms 40
2.1. Convergence groups 40
2.2. Group action on the discontinuity set 54
2.3. Fundamental domains 62
2.4. Convex polyhedra and reflection groups 77
2.5. Discrete group action on the limit set 86
Notes 100
3. Basics of Hyperbolic Groups and Manifolds 101
3.1. Margulis's Lemma and splittings of hyperbolic manifolds 101
3.2. Injectivity radius of hyperbolic manifolds 107
3.3. Thin cusp submanifolds Ill
3.4. Precisely invariant horoballs 117
3.5. Group action on the set of horoballs 121
3.6. Convex hull constructions 123
3.7. Tessellations of manifolds by ideal hyperbolic polyhedra 129
xii Table of Contents
3.8. Hyperbolic arithmetics 130
3.9. Arithmetic groups generated by reflections 133
3.10. Non arithmetic groups of Gromov and Piatetski Shapiro 140
3.11. Fibonacci manifolds 144
Notes 151
4. Geometrical Finiteness 153
4.1. Classical finiteness for planar Kleinian groups 153
4.2. Geometrical finiteness in higher dimensions 156
4.3. Equivalent definitions of geometrical finiteness 166
4.4. Geometrically finite ends and coverings 175
4.5. Geometry of tessellations 178
4.6. Cayley graphs and geometric isomorphisms of discrete groups 191
4.7. Geometrical finiteness for discontinuity set components 204
Notes 215
5. Kleinian Manifolds 217
5.1. Basic topology related to Kleinian manifolds 217
5.2. Topological aspects of combination theorems 225
5.3. Universal groups and Poincare Conjecture 241
5.4. Ends of Kleinian manifolds, their compactification
and Ahlfors's Conjecture 244
5.5. Kleinian n manifolds and hyperbolic cobordisms 256
5.6. Finiteness problems for Kleinian n manifolds 276
Notes 288
6. Uniformization 289
6.1. Classical uniformization 290
6.2. Modern concepts of uniformization 291
6.3. Hyperbolization of manifolds and hyperbolic volumes 308
6.4. Uniformizable conformal structures 324
6.5. Conformal uniformization of "flat" connected sums 335
6.6. Conformal uniformization of Seifert manifolds 342
6.7. Torus sums of conformal structures 350
6.8. Canonical Riemannian metric on conformal manifolds 355
Notes 377
7. Theory of Deformations 379
7.1. Deformations of geometric structures 379
7.2. Rigidity of hyperbolic structures 392
7.3. Quasi Fuchsian structures: bendings 408
7.4. Quasi Fuchsian structures: cone deformations 425
Table of Contents xiii
7.5. Bendings along surfaces with boundaries 434
7.6. Global properties of deformation spaces 441
Notes 457
Bibliography 461
Index 513 |
| any_adam_object | 1 |
| author | Apanasov, Boris Nikolaevič 1920- |
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| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-09-27T08:01:26Z |
| institution | BVB |
| isbn | 3110144042 |
| language | English |
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| physical | XIII, 523 S. graph. Darst. : 25 cm |
| publishDate | 2000 |
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| publishDateSort | 2000 |
| publisher | <<de>> Gruyter |
| record_format | marc |
| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Apanasov, Boris Nikolaevič 1920- Verfasser (DE-588)105576724X aut Conformal geometry of discrete groups and manifolds by Boris N. Apanasov Berlin ; New York <<de>> Gruyter 2000 XIII, 523 S. graph. Darst. : 25 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 32 Literaturverz. S. 461 - 511 Groupes discrets ram Géométrie conforme ram Variétés (Mathématiques) ram Conformal geometry Discrete groups Manifolds (Mathematics) Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Diskrete Gruppe (DE-588)4135541-6 gnd rswk-swf Ähnlichkeitsgeometrie (DE-588)4205668-8 gnd rswk-swf Ähnlichkeitsgeometrie (DE-588)4205668-8 s Diskrete Gruppe (DE-588)4135541-6 s Mannigfaltigkeit (DE-588)4037379-4 s DE-604 De Gruyter expositions in mathematics 32 (DE-604)BV004069300 32 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009061164&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Apanasov, Boris Nikolaevič 1920- Conformal geometry of discrete groups and manifolds De Gruyter expositions in mathematics Groupes discrets ram Géométrie conforme ram Variétés (Mathématiques) ram Conformal geometry Discrete groups Manifolds (Mathematics) Mannigfaltigkeit (DE-588)4037379-4 gnd Diskrete Gruppe (DE-588)4135541-6 gnd Ähnlichkeitsgeometrie (DE-588)4205668-8 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4135541-6 (DE-588)4205668-8 |
| title | Conformal geometry of discrete groups and manifolds |
| title_auth | Conformal geometry of discrete groups and manifolds |
| title_exact_search | Conformal geometry of discrete groups and manifolds |
| title_full | Conformal geometry of discrete groups and manifolds by Boris N. Apanasov |
| title_fullStr | Conformal geometry of discrete groups and manifolds by Boris N. Apanasov |
| title_full_unstemmed | Conformal geometry of discrete groups and manifolds by Boris N. Apanasov |
| title_short | Conformal geometry of discrete groups and manifolds |
| title_sort | conformal geometry of discrete groups and manifolds |
| topic | Groupes discrets ram Géométrie conforme ram Variétés (Mathématiques) ram Conformal geometry Discrete groups Manifolds (Mathematics) Mannigfaltigkeit (DE-588)4037379-4 gnd Diskrete Gruppe (DE-588)4135541-6 gnd Ähnlichkeitsgeometrie (DE-588)4205668-8 gnd |
| topic_facet | Groupes discrets Géométrie conforme Variétés (Mathématiques) Conformal geometry Discrete groups Manifolds (Mathematics) Mannigfaltigkeit Diskrete Gruppe Ähnlichkeitsgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009061164&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004069300 |
| work_keys_str_mv | AT apanasovborisnikolaevic conformalgeometryofdiscretegroupsandmanifolds |